Titlebook: Approximation Methods in Probability Theory; Vydas ?ekanavi?ius Textbook 2016 Springer International Publishing Switzerland 2016 character

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Absolutely Continuous Approximations,For absolutely continuous distributions it is more convenient to write all results in terms of distribution functions. We recall that the distribution function of . is . and . Here .(.) is a nonnegative function integrable on the real line, called the density of?..

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,Heinrich’s Method for m-Dependent Variables,In this chapter, we present Heinrich’s adaptation of the characteristic function method for method Heinrich’s weakly dependent random variables. Though the method can be applied for various dependencies (see the bibliographical notes at the end of the chapter) we consider m-dependent random variables only.

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0172-5939 ny exercises with solutions as well as bibliographical notes.This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions a

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https://doi.org/10.1007/978-3-322-90973-2 characteristic function method for the Kolmogorov norm, which is usually associated with the names of Esseen and Le?Cam. It allows us to compare distributions with different structures under the existence of moments of low order or even when no finite moment exists.

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Textbook 2016 Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximatio